Rapid and accurate ambiguity resolution is the core of high-precision precise point positioning (PPP) data processing. However, the ambiguity parameters in PPP observation models are easily affected by atmospheric residual and gross errors, which lead to the probability of successfully fixing decreases and computational burden increases in full ambiguity resolution. Therefore, an increasing number of partial ambiguity resolution (PAR) strategies have been proposed. The selection of the optimal subset of PAR is crucial in this method. The traditional optimal subset selection method of PAR commonly leads to a single judgment criterion and weakened geometric configuration strength because the satellites with low elevation angles are often easily eliminated during the optimal subset selection. In this paper, a multi-factor constrained optimal subset selection method for PAR was proposed, which incorporates the ambiguity variance, the ambiguity dilution of precision (ADOP), satellite position dilution of precision (PDOP) and ratio test values. In order to verify the feasibility of the proposed optimal subset selection method, PAR tests under two schemes were performed for GPS/Galileo based on the static observation data of 15 Multi-GNSS Experiment (MGEX) tracking stations. The results show that, compared with the ambiguity variance sorting method, the proposed subset selection method can further improve the accuracy of the coordinate solution and the strength of geometric figure positioning. The average root mean square of the coordinate residuals is found to decrease by about 12.90%, 6.83% and 9.39% in the eastern, northern and vertical directions, respectively. The increase in the fixed epoch rate ranged from 0.87% to 33.33%, with an average of about 8.71%.

High-precision DCBs are essential for effective multi-frequency and multi-constellation GNSS integration, especially in processing compatible signal observations. This study utilizes data from MGEX, iGMAS, and CORS stations to estimate and analyze long time series of BDS/GNSS DCBs, focusing on stability and influencing factors. Results indicate that DCBs for the same signal, but different channels exhibit similar ranges and trends. Among BDS DCBs, those from satellites with rubidium atomic clocks are more stable than those with hydrogen atomic clocks. An upgrade and maintenance of BDS in late 2022, reported by NABU, likely contributed to DCB jumps. BDS-compatible signal DCBs show weaker stability compared to GPS and Galileo. Variations in GNSS signal processing and receiver algorithms also impact DCB stability. Converting DCBs to OSBs and performing RMS statistics revealed that smaller differences between signals increase the susceptibility of observation equations to observation quality.

Atmospheric pressure loading (APL) deformation is one component of nontectonic deformation for Global Navigation Satellite System (GNSS) time series and is a kind of deformation response caused by a redistribution of atmospheric pressure. In this paper, we present an atmospheric data processing strategy to compute the APL based on a spherical harmonic expansion of the global atmosphere pressure changes. We also provide a sample model to describe the relativity between the global atmosphere pressure changes and APL vertical deformation. The results show that the variation of air mass has a major impact on the north-eastern area of East China, the eastern area of North China, and Northeast China, and the vertical crustal displacement caused by the atmosphere changes in these regions can reach about 20 mm. The correction of APL for vertical time series of GNSS reference stations in different regions indicates that the arid area of the Northwest China, Northeast China, Central China, and North China are greatly affected by APL. While for the station located in Sichuan-Yunnan region, the amplitude and period change are small after correction of APL for vertical time series of GNSS reference stations, which reveals that the area is seriously affected by tectonic movement and water migration loading. The correlation between atmospheric pressure changes and crustal deformation is analyzed, which shows that APL has a serious impact on the north-eastern area of North China, the Northeast China, and the eastern area of Central China when the variations in atmospheric pressure in mainland China are the same. The research results of this paper will provide some reference value for the study of crustal structural deformation and the establishment of geodetic datum.

The time-varying biases within carrier phase observations are integrated into satellite clock offset parameters for precise clock estimation. Consequently, when the precise satellite clock bias is applied to the third frequency observation for precise point positioning (PPP), a new type of inter-frequency clock bias (IFCB) with satellite dependence should be noticed. If the IFCB is estimated together with the receiver coordinates, tropospheric wet delay, ambiguity and other parameters, it will increase the computational burden and lead to more time consumption. In order to solve this problem, the IFCB of GPS Block IIF satellites were estimated using 162 global uniformly distributed Multi-GNSS Experiment (MGEX) stations. By analyzing the time-varying characteristic of each satellite IFCB and combining the lag characteristics of the final ephemeris products, a modeling method of short-term IFCB prediction based on the epoch-by-epoch sliding Pearson autocorrelation function is proposed. The feasibility of this method was verified through the Student’s t-distribution, comparison with the measured IFCB, the posteriori residual of the third frequency carrier phase and the kinematic/static PPP solutions. The results showed that since the IFCB period was not a complete 24 h, the difference in the IFCBs time series on different days was increasingly significant with the passage of lag time, and the correlation constantly decreased. The peak-to-peak amplitudes of the IFCB difference reached 1.13, 3.44, 6.86 and 11.25 cm when the lag time was 1, 9, 19 and 29 days, respectively. In addition, based on the lag characteristic of final precise ephemerides released by the International GNSS Service (IGS) analysis centers, the prediction accuracy of the IFCB was evaluated with a time lag of 7 days. The root mean square of the posteriori residuals at the third-frequency observation decreased by approximately 51.3% compared to that without considering for IFCB correction. The triple-frequency uncombined PPP in the horizontal and vertical directions improved by approximately 33.2% and 17.2% for the static PPP solutions and 50.2% and 39.7% for the kinematic PPP solutions, respectively. In general, the accuracy and convergence time of the triple-frequency uncombined PPP were equivalently improved when the predicted IFCB and the measured IFCB were used.